Is there a shortcut or clever way to solve this one?

[HughJanus]

(OG, p.48) I find this problem really difficult. The explanation in the book gives a really lengthy process for solving it and I’m wondering if anyone has a shorter way.

[HughJanus]

Forgot to attach this. This is the book’s explanation.

[user7048]

Assume the distance between A and B as x

[HughJanus]

Wow thank you, that is super helpful